Chapter 9.10 Trigonometric Ratios

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Chapter 9.10Trigonometric Ratios

• By Arielle Green
• Mod 9

2
Review equations

• Sin
• Cos
• Tan

3
Vocabulary

• Angle of Elevation the angle between an upward
  line of sight and the horizontal
• is the angle of elevation.

A
angle of elevation
Line of sight
B
C
Horizontal line
4
Sample Problem 1

• A girl was walking in the woods when she stopped
  10 ft away from a tree. She spotted a birds nest
  at an angle of elevation of 37. How far up from
  the ground was the birds nest rounded to the
  nearest tenth?

Q
First choose the formula needed for this problem.
We are working with the two legs of the right
triangle, so we will use tan. Set up the formula
and solve for x.
X
37
S
10
R
ft
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Vocabulary

• Angle of Depression - the angle between a
  downward
• line of sight and the horizontal
• lt
  gt
• is the angle of depression.

horizontal line
Angle of depression
X
W
line of sight
Y
Z
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Sample Problem 2

• An airplane pilot is flying over a forest at an
  altitude of 1600 ft. Suddenly, he spots a fire.
  He measures the angle of depression and finds it
  to be 46. How far is the fire, rounded to the
  nearest tenth, from a point on land directly
  below the plane?
• There are two ways to solve this problem. Well
  look at both ways.

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Method 1
D
A
46
Using parallel lines alt. int. ,
ltACB is also 46. Since only the two legs of the
right triangle are being used, the formula must
be Tan .
1600
46
B
C
X
Set up the equation and solve for x. Tan 46
x x 1545.1 ft

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Method 2
D
A
46
Since ltBAC and ltCAD are complementary lts, ltBAC is
44. Only the two legs of the right triangle are
being used, so the formula must be Tan
.
44
1600
B
C
X
Set up the equation and solve for x. Tan 44
X 1600 tan 44 x 1545.1
ft
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Practice problems Round all answers to the
nearest tenth. Round all angles to the nearest
degree.

• 1.) A lighthouse casts a shadow of 55 ft when
  the sun is at an angle of elevation of 67. How
  tall is the lighthouse?
• 2.) A cat was on a cliff when it saw a mouse
  down below at an angle of depression of 25. The
  cliff is 43 ft tall. How far away is the mouse
  from the bottom of the cliff?
• 3.)A 25-foot ladder just reaches a point on a
  wall 24 ft above the ground. What is the angle
  of elevation of the ladder?

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Practice problems

• 4.)

• 5.)

• Two men are on the opposite sides of a tall
  building with the angle of elevation being 30 and
  60 respectively. If the one man is 40 feet away
  from the base of the building, how far away is
  the other man?

• A pole 40 ft high has a shadow the length of 23
  ft at this point in time. Find the angle of
  elevation of the sun.
• Harry was walking along a pier. He stopped when
  he saw a boat on the lake at an angle of
  depression of 22. If the boat is 65 ft away,
  how high, rounded to the nearest tenth, is the
  pier from the water ?

6.)
30
60
x
40
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Answers to the practice problems

• 1.)
• 2.)
• 3.)

x
67
55
65
43
x
25
24
¹
X
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Answers to practice problems (contd)

• 4.)

• 5.)

40
8
x
¹
23.094
23

60
30
x
40
6.)
22
68
x
ft
22
ft
65
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Works Cited

• Rhoad,Richard, George Milauskas, and Robert
  Whipple. Geometry for Enjoyment and
  Challenge. Boston McDougal Little, 2004.
  423-427.
• MathTrigonometry.Syvum. 2008. Syvum
  technologies. 29 May 2008. lt http//www.syvum.co
  m/cgi/online/serve.cgi/mat h/trigo/trig3.sal gt.